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The Erdős number ((:ˈɛrdøːʃ)) describes the "collaborative distance" between mathematician and another person, as measured by authorship of mathematical papers. The same principle has been applied in other fields where a particular individual has collaborated with a large and broad number of peers. The American Mathematical Society provides a free online tool to determine the Erdős number of every mathematical author listed in the Mathematical Reviews catalogue.〔(【引用サイトリンク】title= Collaboration Distance )〕 == Overview == Paul Erdős (1913–1996) was an influential mathematician who spent a large portion of his later life writing papers with a large number of colleagues, working on solutions to outstanding mathematical problems. He published more papers during his lifetime (at least 1,525) than any other mathematician in history.〔 (Leonhard Euler published more total pages of mathematics but fewer separate papers: about 800.)〔(【引用サイトリンク】work=The Euler Archive )〕 Erdős spent a large portion of his later life living out of a suitcase, visiting his over 500 collaborators around the world. The idea of the Erdős number was originally created by the mathematician's friends as a tribute to his enormous output. However, in later years it gained prominence as a tool to study how mathematicians cooperate to find answers to unsolved problems. Several projects are devoted to studying connectivity among researchers, using the Erdős number as a proxy.〔(【引用サイトリンク】title=Erdös Number Project )〕 For example, Erdős collaboration graphs can tell us how authors cluster, how the number of co-authors per paper evolves over time, or how new theories propagate.〔(【引用サイトリンク】title=Facts about Erdös Numbers and the Collaboration Graph )〕 Several studies have shown that leading mathematicians tend to have particularly low Erdős numbers.〔 Original Spanish version in ''Rev. Acad. Colombiana Cienc. Exact. Fís. Natur.'' 23 (89) 563–582, 1999, .〕 For example, only 134,007 mathematicians have an Erdős number, with a median value of 5. In contrast, the median Erdős number of Fields Medalists is 3. Only 7,097 (about 5%) of mathematicians with a collaboration path have an Erdős number of 2 or lower.〔 As time goes on, the smallest Erdős number that can still be achieved will necessarily increase, as mathematicians with low Erdős numbers die and become unavailable for collaboration. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Erdős number」の詳細全文を読む スポンサード リンク
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